Bi-pattern mining of attributed networks

Henry Soldano,Guillaume Santini,Dominique Bouthinon,Sophie Bary,Emmanuel Lazega

doi:10.1007/s41109-019-0144-1

Abstract

Applying closed pattern mining to attributed two-mode networks requires two conditions. First, as in two-mode networks there are two kinds of vertices, each described with a proper attribute set, we have to consider patterns made of two components that we call bi-patterns. The occurrences of a bi-pattern forms an extension made of a pair of vertex subsets. Second, Formal Concept Analysis and Closed Pattern Mining were recently applied to networks by reducing the extensions of pattern to their cores, according to some core definition. We need to consider appropriate core definitions for two-mode networks and define accordingly closed bi-patterns. We describe in this article a general framework to define closed bi-pattern mining. We also show that this methodology applies as well to cores of directed and undirected networks in which each vertex subset is associated with a specific role. We illustrate the methodology first on a two-mode network of epistemological data, then on a directed advice network of lawyers and finally on an undirected bibliographical network.

Highlights

The first motivation of this article is to extend the Closed Pattern Mining (CPM) and Formal Concept Analysis (FCA) methodologies in order to investigate attributed twomode networks
Summary We have briefly presented standard closed pattern mining and FCA together with abstract closed pattern mining in which the support set ext(q) of a pattern q is reduced to its abstract support set p ◦ ext(q) where p is an interior operator
We found bi-patterns made of a single star with null homogeneity, meaning the co-authors of this single star in the core subgraph have at least one common label they do not share with the star

Summary

Introduction

The first motivation of this article is to extend the Closed Pattern Mining (CPM) and Formal Concept Analysis (FCA) methodologies in order to investigate attributed twomode networks. Note that there is no difference between the two methodologies in that they enumerate the same closed patterns, FCA is interested in the structure of this result as a conceptual structure. The present work follows previous work in which CPM and FCA were applied to undirected and directed graphs. In what follows we recall the notions which CPM of attributed networks rely on. The first formal core definition was the k-core subgraph which is the greatest subnetwork whose vertices all have degree at least k in the subnetwork (Seidman 1983). By changing (2019) 4:37 the topological property we obtain various core definitions within the generalized cores framework proposed by V.

Methods

Findings

Conclusion